A group \(\mathbb {G}(A,I)\)  is called a graph group, or
right-angled Artin groupThis term comes from the fact that right-angled Artin groups
are exactly the Artin groups corresponding to right-angled Coxeter groups., or free partially commutative group.
Here, we use the term graph group.
Graph groups received a lot of attention in group theory during the last years, mainly
due to their rich subgroup structure [1]}, [2]}, [3]}, and their relationship to low dimensional
topology (via so-called virtually special groups) [4]}, [5]}, [6]}.
